He may be a Hollywood actor starring in a glossy TV drama, but Matthew Rhys is still an ordinary Welsh lad at heart, worrying about the Six Nations. The tournament is not, however, a big concern in Los Angeles, where he has lived for five years. "It's not that they don't get rugby," he says. "It's that they have absolutely no idea it exists."

Rhys, aged 36, has been out west working with Sally Field, Rob Lowe and Calista Flockhart on Brothers and Sisters, which airs here on More4. His portrayal of Kevin Walker, an acerbic, gay California lawyer, is one of the best things about the show – an articulate family drama that occasionally threatens to tip over into sentimental mush. Often, Kevin alone brings it back from the brink.

But it's Wales that exerts the strongest creative pull on Rhys. It informs almost all his other work, from his portrayal of Dylan Thomas in 2008's The Edge of Love, to a recent pilgrimage he made across Patagonia on horseback with descendents of the region's original Welsh settlers; he documented the latter in a book published last year. And now he's starring in Patagonia, a new film out tomorrow.

The part came about through a remarkable coincidence. While out on his gruelling trip through Patagonia, the spectacular geographic region located in Argentina and Chile, he bumped into the Welsh director Marc Evans, who was scouting for locations. "I thought I was going mad," says Rhys. "Marc's wife Nia [Roberts, who also stars in the film] ran up alongside me and said, 'Hiya, Math.' I almost fell off my horse."

Rhys plays Mateo, an Argentinian of Welsh descent who comes between an unhappy couple. In a parallel story, an Argentinian grandmother visits Wales, where her mother was born; she's accompanied by a young neighbour, Alejandro. The film also marks singer Duffy's not-half-bad debut, as a student who catches Alejandro's eye. "We were filming in the desert," says Rhys, "and had to bunk down in a concrete barn. But there was great camaraderie – we got arseholed on cheap red wine every night."

Why do Welsh stories exert such a pull? "We're sometimes treated like the stupid cousin, so I'm always drawn to characters that make you feel good about being Welsh," he says. "This was a great opportunity to play a rare character for a Welshman. The challenge was to play someone who speaks a very different type of Welsh, influenced by another country and language."

Rhys first picked up film and TV work while still studying at Rada. After graduation, major roles included Benjamin in 2000's acclaimed West End production of The Graduate, opposite Kathleen Turner, and the lead in the BBC's lavish dinosaur epic, The Lost World. After a comfortable five years of Brothers and Sisters, he is starting to crave this variety again.

"It's nice to have some security," he says. "You get used to that life. But it's a bit like an office job: I go to the same place every day, park in the same spot, turn up in shorts and flip-flops and then put on a suit. Part of me misses the variety that comes with not knowing what you're going to do next."

He has also started to take more creative control, directing episodes of the TV show. He now has five episodes – three in the current series – under his belt. "I find it gratifying. Everyone turns to you for answers and you think, wow, I have an opinion on how this looks, what happens, the tone. And being treated like a grownup is nice."

Despite being based on the other side of the world, Rhys is a passionate supporter of UK arts causes, publicly bemoaning the demise of the Film Council and even backing a campaign to save a threatened theatre in Pembrokeshire. But he isn't hurrying back to the UK. "So little film or TV drama is being made in the UK that I do see myself [in LA] for a little," he says. "Ultimately, you have to go where the work is."

So what's next? "It's weird how your perspective changes," he says. "At the start of your career, you think, 'I just want to do cutting-edge work that makes people think.' Now, I would do a blockbuster in a heartbeat." What changes? "Just awareness of what we do. Don't get me wrong, I take it very seriously and work hard. But at the end of the day, we're entertainers."

• Patagonia is out tomorrow. Brothers and Sisters is on More4 on Thursdays.